Changing a name in new york?

I live in upstate new york and i wanting to change my 13 year old daughters name before school starts. She goes by her middle name ,so we just want to switch them around. What is the process to doing this? Will it be done before school starts? ( sept. 8 ) Should i just go to the court and get the papers to fill out or should we use legal zoom? Which one is faster, cheaper, and easier? Thanks!